The higher the lift-to-drag ratio (L/D ratio) of the wings of an aircraft, the more efficiently the aircraft may fly with less fuel consumption. One method to improve the L/D ratio of an airplane is to use a wing of greater span or length and shorter chord or distance from a leading edge of the wing to a trailing edge of the wing. In other words a wing with greater aspect ratio will have a higher L/D ratio and will be more efficient. Aspect ratio is defined as the wing span squared divided by the wing area. Several practical considerations may limit the degree to which aspect ratio may be increased. One limitation may be airport compatibility. Airports may be designed for airplanes with a certain maximum wing span. To operate at an airport, each airplane must have a wing span that is less than or equal to the maximum for the particular airport.
Another possible limitation may be wing weight. The use of a high aspect ratio wing can increase the airplane's L/D ratio but may not result in lower drag and may not result in less fuel consumption. Because the wing is a structural element, increasing its length increases the bending load the wing must resist. Accordingly the wing structure must be stronger or more robust to resist the bending load. The increased structure increases the wing's weight. Thus, a higher aspect ratio may result in a heavier airplane. Because drag is equal to airplane weight divided by the L/D ratio, a higher airplane weight may result in increased drag even if the L/D ratio is increased. In practice, wing aspect ratios are set to a value that results in minimum drag, or the aspect ratios are set to lower values that result in a significantly lighter airplane with drag that is slightly greater than minimum.
Another limitation to designing an aircraft wing with a higher L/D ratio or a higher aspect ratio may be wing flutter. Wing flutter is a dynamic phenomenon in which an approximately vertical (flapping) motion of the wing couples with a torsional mode (wing twist), resulting in unacceptable shaking in the wing that can cause structural damage. Wings can become more limber at higher aspect ratios which can lead to greater flutter susceptibility. This relationship sometimes limits the wing aspect ratio.
One existing method to alleviate the limitations discussed above is the use of a winglet at each wing tip. FIG. 1 illustrates an aircraft 100 including wings 102 and an aft-swept winglet 104 attached to a wing tip of each wing 102. The winglet 104 may provide the benefit of increased wing span without actually increasing the wing span. Winglets 104 may also reduce the bending load on the wing 102 compared to a conventional wing having an equivalent L/D ratio, thereby reducing the weight penalty of a wing with a larger span. However, especially for higher aspect ratio wings, aft-swept winglets 104 may result in increased flutter susceptibility. The aerodynamic benefit of winglets 104 is increased with increased winglet span, “S,” or distance from a root 106 of the winglet 104 to a tip 108 of the winglet 104, but the structural and especially flutter susceptibility increases rapidly with winglet span. Thus flutter concerns tend to limit winglet span.
One factor affecting wing flutter susceptibility is reduction of the natural twisting frequency of the wing. The wing may be considered to be a torsional pendulum. Resistance to torsion is typically provided by the box or tube-like structure of the wing. Given the torsional rigidity provided by this structure, the frequency is primarily determined by the polar distribution of mass about a torsional axis 110 of the wing structure as well as a spanwise distribution of this mass. As an analogous example, consider a special clock that uses a torsional pendulum consisting of a thin vertical rod fixed to the clock at the top and free at the bottom. At the bottom of this rod a small dumbbell is attached. When this dumbbell is rotated about the axis of the rod, the rod provides torsional resistance. When the dumbbell is released, the dumbbell oscillates at a certain frequency according to its polar moment of inertia about the rod's axis and the rigidity of the rod. An increase in inertia reduces the frequency. Moving the dumbbell to a point midway on the rod will result in an increased frequency because of the higher effective rigidity of the rod. Longer winglets tend to have greater polar moment of inertia by virtue of their greater weight and greater length.
Another factor affecting wing flutter susceptibility is the rearward offset of the wing's mass with respect to the torsional axis 110 of the wing's structure. As the wing flies through the air, it makes lift that is proportional to its angle of attack. Increased lift tends to drive the wing upward, especially the outer portion of the wing. For instance, flying into an upward gust of air directly increases the wing's angle of attack which increases its lift which results in an upward acceleration, resulting in an upward deflection. If the center of mass of the wing is behind the torsional axis of the wing, then this upward gust will result in the wing twisting to a higher angle of incidence. This increases the angle of attack beyond the additional increment from the gust, resulting in an increased deflection. As the wing approaches the top of the stroke, it begins to decelerate. This tends to twist the wing to a reduced angle of attack, driving it downwards with increased force. If the torsional frequency of the wing coincides (or nearly coincides) with the wing bending (flapping) frequency, this oscillation can grow to a proportion that may result in damage to the wing. In general, as airspeeds increase, wing bending frequencies may tend to increase and torsional frequencies may decrease. At some speed these frequencies may coincide, leading to flutter. Wing flutter may also be influenced by fore and aft motions of the wing that are tied to the vertical motions. This type of motion is more likely in slender, high aspect ratio wings.
Aft-swept winglets, such as winglets 104, may increase flutter susceptibility because they may increase the polar moment of inertia of the wing 102 about the wing's torsional axis 110 and the winglets 104 do this at the wing tip, which may be the most undesirable location for such forces. Additionally, aft-swept winglets 104 add weight behind the wing's torsional axis 110 and this weight is also added at the wing tip. Increasing the span of aft-swept winglets 104 may also increase the polar moment of inertia and moves the wing's center of mass aft. Thus, longer winglets may further increase flutter by the two mechanisms described above.
An additional factor that constrains the span of the winglet pertains to ground clearance. Winglets may sweep up from the wing tip or may sweep down, or both. The aerodynamic benefit is approximately driven by the distance from the top of the upper winglet to the bottom of the lower winglet. From a flutter standpoint, the increase in polar moment of inertia would benefit from the upper and lower winglets having the same span. This puts the center of mass of the upper and lower winglets closer to the wing's torsional axis 110. Also, the center of mass of the winglets as a system is farther forward than if only a single winglet of the same span is used. Both the reduction in polar moment of inertia and forward offset of the center of mass reduces flutter susceptibility. However, the length of a lower winglet is limited by ground clearance. It is important that the winglet not contact the ground in any ordinary operation including landing and takeoff. Roll clearance is usually most critical when the airplane is pitched up for takeoff or landing. In this nose-up position, a lower aft swept winglet, especially when mounted on an aft swept wing, is closer to the ground by virtue of its more aft location. This means that a lower aft-swept winglet is relatively more constrained in span than an unswept winglet.
Accordingly, there is a need to improve the L/D ratio and performance of the wings of aircraft to improve efficiency and reduce fuel consumption. As described above, one technique to alleviate the limitations associated with a higher L/D ratio or a higher wing aspect ratio is the use of winglets. However, any winglet configurations need to avoid flutter susceptibility and other issues similar to those described above.